This invention relates generally to active filters, and more particularly to filters employing frequency dependent negative resistors (FDNRs) useful in telephone carrier and signalling equipment.
Generally speaking, filters are used to separate desired signals from undesired signals, and they are extensively employed in telephone carrier equipment. The response of a filter can be mathematically expressed by means of a transfer function. In general, a designer knows the defining limits of the transfer function that is required; and filter tables can be searched to determine what passive inductance and capacitance ladder network satisfies this requirement. Additional references are available which allow the designer to construct the transfer function of the filter so chosen. Once the transfer function is known, the filter can be synthesised by an infinite number of RLC topologies. However, most of these topologies must use inductors which are expensive, bulky and less desirable than resistors and capacitors.
It has been known for some time that any transfer function realizable with passive resistors, capacitors, and inductors can be attained with amplifiers, resistors, and capacitors. To do this, one creates a topology that gives a transfer function of the same form as the passive RLC network. Then, by appropriately equating the coefficients, one creates a set of equations that can be solved to give appropriate values for the resistors, capacitors, and amplifier gains. There is no limit to the number of topologies that can be created, and the more common ones were proposed in a paper by Sallen and Key. However, all such topologies suffer a common shortcoming, which is high component sensitivities. With filters such as Cauer types, the requirements placed upon component accuracies to synthesize the transfer function accurately are formidable. This means a high manufacturing cost for the filters. It has been suggested by L. T. Burton that a better approach would be to scale a passive RLC network by multiplying all terms by 1/S. This transformation does not change the transfer function but transforms inductors into resistors, resistors into capacitors, and capacitors into frequency dependent negative resistors (FDNR).